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Finding the Third Proportional to 13,830 and 16,806

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Solution

The third proportional to 13,830 and 16,806 is: 20,422.39

Step by Step Solution

  1. Step 1: Write the proportion equation
    13,830 : 16,806 = 16,806 : x
  2. Step 2: Convert to fraction form
    13,830/16,806 = 16,806/x
  3. Step 3: Cross multiply
    13,830x = 16,806 × 16,806
  4. Step 4: Simplify right side
    13,830x = 282,441,636
  5. Step 5: Solve for x
    x = 282,441,636/13,830
  6. Step 6: Final answer
    x = 20,422.39

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Why These Related Problems?

These problems maintain the same ratio (1.22) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.